To simplify the ratio \(85:561\), we need to find the greatest common divisor (GCD) of the two numbers and then divide both numbers by the GCD.

Let's calculate the GCD of 85 and 561.

**Prime Factorization Method:**

1. **Prime Factors of 85:**  
   85 = 5 × 17

2. **Prime Factors of 561:**  
   561 = 3 × 11 × 17

The common factor between 85 and 561 is 17.

**Simplification:**

Now, divide both numbers by 17:

\[
\frac{85}{17} = 5, \quad \frac{561}{17} = 33
\]

So, the simplest form of the ratio \(85:561\) is:

\[
\boxed{5:33}
\]

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you find the GCD of two numbers using the Euclidean algorithm?
2. How do you simplify a ratio involving larger numbers?
3. What are the applications of simplifying ratios in real-life situations?
4. How do you simplify ratios when given in fraction form?
5. How can you check if a ratio is already in its simplest form?

**Tip:** When simplifying ratios, always look for the greatest common factor to reduce the ratio effectively.

Learn how to simplify the ratio 85:561 by finding the greatest common divisor (GCD). Using prime factorization, we reduce the ratio to its simplest form, 5:33. This step-by-step explanation is ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation